Ultra-wideband technology has good anti-interference capabilities and development prospects in indoor positioning. Since ultra-wideband will be affected by random errors in indoor positioning, to exploit the advantages of the Kalman filter (KF) and the long short-term memory (LSTM) network, this paper proposes a long short-term memory neural network algorithm fused with the Kalman filter (KF–LSTM) to improve UWB positioning. First, the ultra-wideband data is processed through KF to weaken the noise in the data, and then the data is fed into the LSTM network for training, and the capability of the LSTM network to process time series features is employed to obtain more accurate label positions. Finally, simulation and measurement results show that the KF–LSTM algorithm achieves 71.31%, 37.28%, and 49.31% higher average positioning accuracy than the back propagation (BP) network, (back propagation network fused with the Kalman filter (KF-BP), and LSTM network algorithms, respectively, and the KF–LSTM algorithm performs more stably. Meanwhile, the more noise the data contains, the more obvious the stability contrast between the four algorithms.